发表机构
School of Physics, Sun Yat-Sen University（中山大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究方格SU(N)非阿贝尔规范场系统，发现大陈数平带和狄拉克锥的奇偶结构，并揭示非常规超流相，为拓扑物理提供新平台。
AI 中文摘要
我们研究了具有均匀SU($N$)非阿贝尔规范场的二维方格系统中的拓扑能带结构和超流相。从与通量$\alpha=1/4$的Hofstadter模型相关的SU(4)规范场模型出发，我们证明了最低和最高能带是孤立的陈能带，携带陈数$C=-4$，并在条带几何结构中产生四个手性边缘模。值得注意的是，尽管两个中间能带接触并形成$16$个无间隙狄拉克锥，它们的组合陈数为$C=8$。然后我们将构造推广到SU($N$)系统，并揭示了能带拓扑的奇偶结构：当$N$为奇数时，所有能带都是孤立的并携带非零陈数；当$N$为偶数时，两个中间能带在$N^{2}$个狄拉克点处接触，而所有其他能带保持孤立且拓扑非平凡。我们发现随着$N$的增加，最上层和最下层能带变得越来越平坦，其贝里曲率变得更加均匀，为实现分数量子陈绝缘相提供了一个有前景的平台。我们进一步研究了具有在位吸引Hubbard相互作用的自旋-$3/2$ SU(4)模型，探讨了其在部分填充下的超流相。我们发现非阿贝尔规范场打破了五重态配对的隐藏SO(5)简并性，并选择了不同的向列超流态。对于中间能带区域的填充，所得谱可以承载拓扑保护的Bogoliubov费米面。我们的结果为在合成SU($N$)冷原子系统中探索拓扑能带物理和非常规超流性提供了一个起点。
英文摘要
We study topological band structures and superfluid phases in two-dimensional square-lattice systems with homogeneous SU($N$) non-Abelian gauge fields. Starting from an SU(4) gauge-field model related to the Hofstadter model with flux $α=1/4$, we show that the lowest and highest bands are isolated Chern bands that carry Chern numbers $C=-4$ and give rise to four chiral edge modes in a strip geometry. Remarkably, although the two middle bands touch and form $16$ gapless Dirac cones, their combined Chern number is $C=8$. We then generalize the construction to SU($N$) systems and reveal an even--odd structure of the band topology: when $N$ is odd, all bands are isolated and carry nonzero Chern numbers; when $N$ is even, the two middle bands touch at $N^{2}$ Dirac points, while all other bands remain isolated and topologically nontrivial. We find that the uppermost and lowermost bands become increasingly flat and their Berry curvature becomes more uniform as $N$ increases, providing a promising platform for realizing fractional Chern insulating phases. We further examine the spin-$3/2$ SU(4) model with on-site attractive Hubbard interactions, exploring its superfluid phases at partial filling. We find that the non-Abelian gauge field breaks the hidden SO(5) degeneracy of the quintet pairing and selects distinct nematic superfluid states. For fillings in the middle-band regime, the resulting spectrum can host topologically protected Bogoliubov Fermi surfaces. Our results provide a starting point for exploring both topological band physics and unconventional superfluidity in synthetic SU($N$) cold-atom systems.
Comments13 pages, 6 figures
